Black Hole At The Center Of The Earth

[RandyD123]

If the Earth were hollow and we only had the shell could a black hole at the center take the place of all the mass and provide us with gravity to keep us from floating away?

 

[Dale]

Yes. (Ignoring the mechanical issues)

 

[Ibix]

Well - the system is unstable because the shell exerts no gravitational force on objects inside itself (Gauss' Theorem). So the first time a micro-meteor crashes into the outer surface the shell will drift relative to the black hole until they collide. So it would fairly rapidly become apparent to an observer on the surface what was going on. Also, the shell may not be strong enough to support itself against 1g in the first place, as Dale alludes. Also, I don't know how an Earth-mass black hole would form in the first place.

So, the answer is an extremely qualified yes. The gravitational field from a point mass plus a concentric shell is the same outside the shell as any other spherically symmetric mass distribution with the same total mass contained within the same volume. However, the two will not remain concentric for long, for various reasons.

 

[Stephanus]

If the Earth were hollow and we only had the shell could a black hole at the center take the place of all the mass and provide us with gravity to keep us from floating away?

Yes. (Ignoring the mechanical issues)

Wouldn't the shell will orbit the center of the earth, considering it's 6200 km hollow space. 5 mm radius for Earth mass black hole, right?
And wouldn't there be a shell at all? I think the shell will orbit the center in all 3 dimensions not like orbital plane.

 

[Ibix]

Wouldn't the shell will orbit the center of the earth, considering it's 6200 km hollow space. 5 mm radius for Earth mass black hole, right?

The shell isn't orbiting. It completely encloses a large volume of space with a black hole at the centre, yes. But it is not necessarily rotating at orbital speed, and is prevented from collapsing by its own mechanical strength, which may not be up to the task.

And wouldn't there be a shell at all? I think the shell will orbit the center in all 3 dimensions not like orbital plane.

I'm not sure what this is meant to mean. As noted, the shell isn't necessarily orbiting. If it were, it can't be orbitting in 3 dimensions. A spin has an axis.

 

[Dr_Zinj]

Not sure why you'd want a planetary shell of 6000 miles around an Earth-mass black hole; unless you were planning on a planet-sized Dyson sphere and were going to use a controlled drop of mass into the hole for power generation.

Geophysics has pretty much ruled out the existence of Pellucidar.

 

[Stephanus]

Not sure why you'd want a planetary shell of 6000 miles around an Earth-mass black hole; unless you were planning on a planet-sized Dyson sphere and were going to use a controlled drop of mass into the hole for power generation.

Geophysics has pretty much ruled out the existence of Pellucidar.

4000 miles or 6000 km (40000/pi/2 = 6300 km)

 

[Fervent Freyja]

Is there really any experimental evidence showing this could be true? All those yeses you guys are giving might encourage news stories like this...

A[/PLAIN] more frightening scenario is the black hole may not be stationary.

Although a singularity could sit dead center inside the Earth's spinning, molten core, others have suggested that a small black hole might bounce back and forth beneath the mantle like the clapper of a bell.

As the hole approached the surface it would be attracted back to the center of the planet, fall inward, build up speed, and slip right through the core to the other side of the Earth.

The "ringing" process could be repeated for thousands, even millions, of years until enough matter had been swallowed by the hole to destroy the Earth.

When the hole began the process of swallowing the Earth most of the planet would be gone within a matter of hours.

Dramatic.

 

[Dale]

Is there really any experimental evidence showing this could be true?

There is no experimental evidence supporting the idea that the Earth is hollow, and it is contradicted by a large body of evidence.

 

[Stephanus]

I'm sorry. Beside Kola deep hole, I think there many experiments, if not result, to show that the Earth is not hollow? The wave pattern from seismographs, don't they show that the Earth has layers of cores? The S wave and P wave.

 

[Fervent Freyja]

There is no experimental evidence supporting the idea that the Earth is hollow, and it is contradicted by a large body of evidence.

That's what I figured. If my nephew saw this thread he would insist there is indeed a black hole at the center of the earth.

 

[Ibix]

Is there really any experimental evidence showing this could be true?

The gravitational field of a black hole surrounded by a concentric spherical shell is indistinguishable from that of any other spherically symmetric mass distribution with the same total mass and radius. However, the system is not stable and the first time a gnat sneezed anywhere near it the game would be up. The shell would drift with respect to the black hole and the gravitational field at the surface would change measurably.

Aside from that, as others have noted, there is a lot of seismological evidence that the Earth is not hollow. In short, we can "hear" shock waves from earthquakes traveling along the surface of the Earth, notably because they sometimes flatten buildings. But seismographs on the other side of the planet can also hear waves traveling through the body of the Earth, which they wouldn't be able to if it were hollow. In fact, studying the arrival times of such waves is how we know anything about the interior of the Earth.

Black holes are very cold, but the interior of the Earth is hotter than the surface, which has been verified in deep mines. Also, volcanoes exist. In a similar vein, it is hard to see how continental drift could work with a shell - what would the plates be floating on?

And how does the system form? The Chandrasekhar mass, the minimum mass for something to collapse into a black hole under its own weight, is larger than the mass of the Sun. The Earth is a pebble in comparison.(Edit: error corrected by @PeterDonis, below)

In short, although the gravitational field of a black hole plus a shell is the same, pretty much everything else would be different. And the gravitational field wouldn't stay the same for very long - certainly not the four billion years our planet has been around.

 

[PeterDonis]

The Chandrasekhar mass, the minimum mass for something to collapse into a black hole under its own weight

This is not a correct definition of the Chandrasekhar mass. The correct definition is that it is the maximum mass that a white dwarf can have. But an object heavier than that could still collapse into a neutron star, not a black hole; the maximum mass limit for neutron stars is not known precisely, but it is known to be somewhat larger than the Chandrasekhar mass.

Second, the fact that a black hole lighter than the maximum mass limit (for neutron stars) can't form by ordinary gravitational collapse of a massive object does not mean such a hole could not form by some other means. We don't know of any obvious way for that to happen, but that's very different from being confident that it could not happen.

None of this affects your other points; it is certainly true that we have abundant evidence that the Earth is not hollow and does not have a black hole inside it.